| Safe Haskell | None |
|---|---|
| Language | GHC2024 |
Circuit.Mat.Complex
Description
Complex multiplication as a structure-constant contraction in
Circuit.Mat.
A complex number is a vector (F 2 -> s): slot 0 is real, slot 1 is
imaginary. The product is the contraction of the outer product against the
structure-constant tensor of R[x]/(x² + 1).
Synopsis
- complexSMul :: (Additive s, Multiplicative s, Subtractive s, Eq (F 2), Eq (F 2, F 2), Finite (F 2, F 2)) => (F 2 -> s) -> (F 2 -> s) -> F 2 -> s
- structureConst :: (Additive s, Multiplicative s, Subtractive s) => F 2 -> F 2 -> F 2 -> s
Documentation
complexSMul :: (Additive s, Multiplicative s, Subtractive s, Eq (F 2), Eq (F 2, F 2), Finite (F 2, F 2)) => (F 2 -> s) -> (F 2 -> s) -> F 2 -> s Source #
Complex multiplication as a Mat contraction.
complexSMul a b k returns component k of the product of the two complex
numbers a and b.
structureConst :: (Additive s, Multiplicative s, Subtractive s) => F 2 -> F 2 -> F 2 -> s Source #
Structure-constant tensor for ℂ = R[x]/(x² + 1).
c k i j is the coefficient of a[i] * b[j] in output component k.